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Burn-in is a method of ‘elimination’ of initial failures (infant mortality). In the conventional burn-in procedures, to burn-in a component or a system means to subject it to a fixed time period of simulated use prior to actual operation. Then those which fail during the burn-in procedure are scrapped and only those which survived the burn-in procedure are considered to be of satisfactory quality. Thus, in this case, the only information used for the elimination procedure is the lifetime of the corresponding item. In this paper we consider a new burn-in procedure which additionally employs a dependent covariate process in the elimination procedure. Through the comparison with the conventional burn-in procedure, we show that the new burn-in procedure is preferable under commonly satisfied conditions. The problem of determining the optimal burn-in parameters is also considered and the properties of the optimal parameters are derived. A numerical example is provided to illustrate the theoretical results obtained in this paper.

This paper presents two regression models to describe the effect of various operating conditions on the reliability of complex mechanical systems subject to deterioration and undergoing minimal repairs, whose failure intensity tends to a finite bound as the system ages. Maximum likelihood estimates of the model parameters and of reliability characteristics are provided. Approximate confidence intervals, based on asymptotic results, are also given. Numerical applications of the proposed models and a related inferential procedure applied to real data sets are provided.

This paper presents a stochastic model developed to describe the reliability-growth of advanced technological systems during a planned on-service period, at the end of which the supplier has to demonstrate the conformity of system reliability to the contractual target. Purchase contracts of such systems generally regard a fleet of units (e.g., a fleet of new traction units for railway or subway service, airplanes, buses, …) so that the development programs are carried out on several system's copies, often put on service in batches during the development program. Thus, heterogeneity over units' reliability often arises, as a consequence of different scheduling of the improving activities. Hence, a stochastic reliability-growth model able to reveal heterogeneity was developed. This model was applied to the electrical equipment of a fleet of locomotives built by Ansaldo Breda for the Italian railway transport company. A graphical goodness-of-fit method shows the adequacy of the model to describe the observed reliability-growth process of a single locomotive. Again, a testing procedure was developed in order to reveal possible heterogeneity over the locomotives of the whole fleet and, hence, on the basis of the revealed heterogeneity, a mixed Poisson reliability-growth (MPRG) model was proposed to describe the reliability-growth process of a randomly selected locomotive of the fleet. Then, the probability of demonstrating the observance of the contractual obligations at the end of the development period was predicted on the basis of the failure data collected during the whole development program. Moreover, a procedure was proposed to test, before the development program is terminated, whether the planned remaining time is sufficiently long to assure a high probability of demonstrating the attainment of the reliability target at the end of the program.

In the failure pattern of repairable equipment subjected to reliability deterioration with operating time, the repeated application of the repair actions sometimes produces a finite bound for the increasing failure intensity. In this paper, a non-homogeneous Poisson process for which the failure intensity is an increasing bounded function is proposed. The characteristics of the proposed model and the physical meaning of its parameters are discussed. It is shown that the proposed model evolves initially as the power law process with shape parameter equal to 2, and then converges asymptotically to the homogeneous Poisson process, the latter being a limiting form of the proposed bounded intensity model. Maximum likelihood estimates and approximate confidence intervals for the model parameters are given as well as a testing procedure for a time trend. Percentile points of the test statistic are computed by simulation for failure truncated samples, and the power of the proposed testing procedure is evaluated and compared to that of two commonly used tests. Finally, numerical examples are given to illustrate the proposed model and related inference and testing procedures.